Two - Chapter Three (six problems) Due: 11/12 #1 Accountants at the firm Walker and Walker believed that several traveling executives submit unusually high travel vouchers when they return from business trips. The accountants took a sample of 200 vouchers submitted from the past year; they then developed the following multiple regression equation relating expected travel cost (Y) to number of days on the road (x1) and distance traveled (x2) in miles: = $145.00 + $64.38 + $1.12 The coefficient of correlation computed was 0.67. (a) If Thomas Williams returns from a 1,056-mile trip that took him out of town for five days, what is the expected amount that he should claim as expenses? (b) Williams submitted a reimbursement request for $1,850; what should the accountant do? (c) Comment on the validity of this model. Should any other variables be included? Which ones? Why? #2 Bus and subway ridership in Washington, D.C., during the summer months is believed to be heavily tied to the number of tourists visiting the city. During the past 12 years, the following data have been obtained: YEAR 1 2 3 4 5 6 7 8 9 10 11 12 NUMBER OF TOURISTS (1,000,000S) 13 7 9 8 19 20 14 16 19 27 21 14 1 RIDERSHIP (100,000s) 18 15 11 22 30 38 34 32 39 52 41 28 (a) Develop a regression model. Please write down the regression equation. (b) What is expected ridership if 35 million tourists visit the city? (c) If there are no tourists at all, explain the predicted ridership. #3 The following data give the starting salary for students who recently graduated from a local university and accepted jobs soon after graduation. The starting salary, grade-point average (GPA), and major (business or other) are provided. SALARY $42,000 $41,500 $37,800 $40,500 $44,000 $31,500 $36,200 $33,200 $41,200 $39,200 $38,700 $42,400 GPA 3.4 3.6 3.5 3.2 3.9 2.1 2.6 3.1 2.8 3.5 3.1 3.6 MAJOR Business Business Other Other Business Other Business Other Business Other Other Business (a) Using a computer, develop a regression model that could be used to predict starting salary based on GPA and major. Please write down the regression equation. (b) Use this model to predict the starting salary for a business major with a GPA of 3.5. (c) What does the model say about the starting salary for a business compared to a nonbusiness major? (d) Do you believe this model is useful in predicting the starting salary? Justify your answer, using information provided in the computer output. #4 The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is better? 2 SELLINMG SQUARE AGE PRICES($) FOOTAGE BEDROOMS (YEARS) 247,600 1,675 2 23 258,000 1,765 3 26 278,600 1,927 3 31 287,100 2,187 3 18 289,100 2,321 3 22 294,600 2,395 3 17 352,600 2,464 3 7 354,600 2,723 4 8 387,600 2,627 3 2 392,100 2,657 4 2 393,600 2,666 3 1 404,600 2,497 3 1 403,100 3,111 4 3 413,600 2,787 4 2 525,100 3,242 5 8 420,600 2,846 4 4 #5 Use the data in problem #4 and develop a regression model to predict selling price based on the square footage, number of bedroom, and age. Use this to predict the selling price of a 2-yearold, 2,870-square-foot house with 4 bedrooms. #6 In 2009, the New York Yankees won 100 baseball games during the regular season. The table on the next page lists the number of victories (W), the earned-run-average (ERA), and the batting average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher number is better. 3 TEAM W ERA AVG New York Yankees 100 4.22 0.294 Los Angeles Angels 97 4.34 0.281 Boston Red Sox 94 4.36 0.285 Minnesota Twins 89 4.48 0.275 Texas Rangers 86 4.42 0.272 Detroit Tigers 85 4.31 0.263 Seattle Mariners 84 4.01 0.259 Tampa Bay rays 83 4.36 0.262 Chicago White Sox 78 4.12 0.254 Toronto Blue Jays 74 4.46 0.269 Oakland Athletics 72 4.23 0.274 Cleveland Indians 65 5.01 0.268 Kanas City Royals 64 4.75 0.263 Baltimore Orioles 62 5.01 0.262 (a) Develop a regression model that could be used to predict the number of victories based on the ERA. (b) Develop a regression model that could be used to predict the number of victories based on the batting average. (c) Which of the two models is better for predicting the number of victories? (d) Develop a multiple regression model that includes both ERA and batting average. How does this compare to the previous models? 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4 Assignment Three - Chapter Four (six problems) Due: 11/19 #1 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 14 months are as follows: SALES ($1,000s) 25 23 22 18 25 27 19 24 30 21 23 22 26 28 MONTH January February March April May June July August September October November December January February (a) Using a moving average with three periods, determine the demand for vacuum cleaners for next March. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would be a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods by MAD. #2 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks: 1 WEEK ACTUAL PASSENGER MILES (1,000s) 1 32 2 34 3 31 4 37 5 28 6 29 7 35 8 33 9 37 10 35 11 34 12 36 (a) Assuming an initial forecast for week 1 of 32,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use = 0.2. (b) What is the MAD for this model? (c) Compute all the RSFE values and tracking signals. Are they within acceptable limits? #3 Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows: WEEK CALLS WEEK CALLS 1 17 13 13 2 15 14 23 3 10 15 11 4 15 16 25 5 18 17 24 6 14 18 16 7 8 19 13 8 11 20 27 9 13 21 29 10 7 22 20 11 9 23 21 12 16 24 25 (a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 17 calls in the first week and use = 0.3. What is the forecast for the 25th week? 2 (b) Reforecast each period using = 0.7. (c) Actual calls during the 25th week were 24. Which smoothing constant provides a superior forecast when the forecast values are compared to the actual value? (Do not carry 24 into the calculations. This question is not asking you to evaluate the MADs.) #4 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 1 205 213 219 228 2 231 236 244 256 3 237 246 258 265 4 274 282 296 307 (a) (b) (c) (d) Compute seasonal indices for each quarter based on a CMA. Deseasonalize the data and develop a trend line on the deseasonalized data. Use the trend line to forecast the sales for each quarter of year 5. Use the seasonal indices to adjust the forecasts found in part (c) to obtain the final forecasts. #5 In the past, Judy Holmes's tire dealership sold an average of 1,056 radials each year. In the past three years, 197, 179 and 193, respectively, were sold in fall, 318, 327 and 311 in winter, 310, 312 and 318 in spring, and 231, 238 and 234 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,120 radials. What will the demand be each season? #6 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991-2013: 3 Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016. Find the R2 for this model. YEAR 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 DJIA 3952 4568 4630 5088 5463 6346 7577 9237 10576 12865 12154 11385 9705 11816 12247 12047 13089 10791 11101 11860 13364 14906 15220 4